Factorials

[@atlas8480]

This channel is not just growing exponentially, its growing factorially

[@sleevman]

Cringe

[@KeshavKumar-zm3lh]

@@sleevman agreed

[@cloudgalaxy9231]

based

[@oeungtichheang2005]

this comment has the same energy as "what do u call two brothers who love math?"

[@webdevacademy3496]

Sad its not the case

[@giosuesavina6611]

You are actually so incredibly good at explaining maths, it's just so cool how you make concepts look so logically easy.

[@helenday5031]

Factorials etc were hurting and puzzling my brain, but after watching this helpful video with its fun gossip about factorials and the factorial personality and landscape and other connections, I feel soothed, happy and cheerful again. Thanks.

[@carl3811]

You're a good teacher. I hope you're still teaching.

[@shreyashkashyap]

The best math teacher I have ever had!

[@grogomeister]

Thank you Professor Woo for rolling out this definition, I've been out of academia for over 10 years but I'll always be a student!

[@alexicazee]

Saw this accidentally while looking for some help for a really difficult sequence (my teacher is developing his own theorem...) and loved it! Great videos!

[@arnav_singh2905]

Was your teacher successful?

[@Dalaz0511]

What did your teacher do?

[@muzafar0438]

Thank you for sharing the knowledge

[@DanteBarboza]

It is way more easy when you put it like that

[@George-kd4ox]

You're the coolest teacher I've ever come across in my life😎!!!!

[@justinotherpatriot1744]

This is the most likable math teacher I've ever seen in my life.

[@MereBaapKiAulaad]

Ponder over this, 1!!!!... = 1 (same for 2, gives 2) 3!!! = infinity 4!!! & 5!!! Also give infinity But from 6 it only take two factorials to get infinity till 170 after that only 1 factorial. I know it seems pretty basic and logical but I'm sure it is possible to give a more deeper and unique approach to this.

[@yasirtaher0919]

Nice Video very enjoyable

[@technus102]

It seems simple ..... Right? :)

[@patrickmayer9218]

*The reason why factorial has an exclamation mark is because it grows faster than other functions (it's excited!). *This is why for comp sci, factorial is worse than expontial runtime. Great video, Mr. Woo!

[@amazing-qq3wi]

Yo who the... actually uses factorial runtime

[@elsa1569]

Thanks for the inspiration! I just started teaching as a side job, and am inspired by your way of explaining these concepts 👏😊

[@jillian2955]

this was on my last test and I had never seen it before. The exclamation was terrifying.

[@SunitaYadav-qj8rz]

That smirk at the end was like, Oh sweetheart this is just the trailer.

[@Aayushh07]

you made me understand this thing at factorial function rate.

[@simgedalgara]

I'm watching from Turkey, it was very useful, thank you.

[@kevinzavalina7030]

I want to be in his class... please God just once!

[@itzz_alexzz]

damn sir u r so good at explaining things easily

[@manavverma7727]

Nice.....🌟

[@farhantajwarahmed3340]

3:43 now that is excitement

[@hayk.galstyan]

You are an awesome teacher!

[@Tarlan_Mammadov]

I cant believe I am watching a math lesson by my own will.

[@hallinden3942]

I love this channel and teacher; however, 0! does not equal 1. The mathematical operation does not hold when you 'count backwards' to 0! Amazing that it is defined to be 0! It is no different than taking a denominator of a fraction and reducing the number to show how large the number is until 0 is reached: at this point 1/0 is not defined as any number in the numerator with 0 in the denominator is undefined. 0! should also be undefined because the mathematical operation breaks-down at this point.

[@Tokmurok]

Yeah I think so too, it’s like 0 consumes the operation which is surprisingly lovecraftian.

[@nuhnur2181]

Hi Mr Eddie Woo.. im Nuh from Indonesia. I want to say THANK YOU VERY MUCH..for all your video.. i just find this and i spend my hole day in a week to watch this channel.. very clear and smart explanation about math.. Umm.. btw, can you show me on what channel i can learn about PHYSICS, that the teacher explanation is Good Like You..? Thanks..God BlessYou..

[@That_One_Guy...]

You can try Khanacademy, it's my compensation of many year of wasting time memorising math formula at schools (beside Zenius, and yes I'm Indonesian too). They give nice derivation of some physics formula that your physics teacher might told to just memorize so you will be like a good little cinnamon calculator (ok that might be a bit overboard), but i dont recommend learning chemistry there too much because there's this one teacher which is kind of textbook based teacher (similar to those type of teacher i mentioned above, his name is Jay) just Zenius is enough for chemistry, it's mostly brilliant even thought most of it's video is long, and Zenius is free to access now by the way ;)

[@fellforfall9802]

If you still need some help with physics, I strongly recommend the organic chemistry tutor!! good luck :)

[@Digital.Academy]

I'm wondering how things grow convolutionally.

[@eeyayacoolguy2014]

Vacations have started and I’m watching math videos...

[@kharoozy]

I love this

[@91dgross]

Wow thanks, this is helping me with recursion and programming. Can you also talk about how it is wrong to say multiplication is repeated addition of a given value? Clearly when we multiply a whole number by a fraction we get a number that has been reduced rather than increased, so repeated addition doesn’t fit for all numbers, sorta like how the first factorial definition here has limits

[@rabuortindi]

needed this for coding....hehe you the best!! :) thanks

[@desahanalam]

Let X,Y,Z and T be intregers with X

[@OrangeDrink]

0,1,-1 are they numbers of a distance from zero or singular representation of the same. Perhaps any physical answers leading from this math need to be adjusted by 1 or negative one to be physically true? Would like to see a tangible example geometry and even then can it's size of n be a problem like with C=√a2+b2 plotted has uncanny results in smaller sizes?

[@GymCritical]

Nice bruh...

[@levistechnology5306]

What are the factorials of negative numbers?

[@andreyvasyaev]

Что мы знаем о факториалах... Для начала мы знаем что факториал следующего числа равен факториалу предыдущего числа умноженному на это самое следующее число... N!= (N-1)!×N или по другому... факториал предыдущего числа равен факториалу следующего числа деленному на это самое следующее число... N!=(N+1)!/(N+1) есть еще вид (N+1)!= N!×(N+1)... значит (N-1)!=N!/N и N=N!/(N-1)! При N=1 получаем 0!=1!/1 и 1=1!/0! При N=0 получаем (-1)!=0!/0 и 0=0!/(-1)! При N=(-1) получаем (-2)!=(-1)!/(-1) и (-1)=(-1)!/(-2)! При N=(-2) получаем (-3)!=(-2)!/(-2) и (-2)=(-2)!/(-3)! При N=(-3) получаем (-4)!=(-3)!/(-3) и (-3)=(-3)!/(-4)! При N=(-4) получаем (-5)!=(-4)!/(-4) и (-4)=(-4)!/(-5)! Видим что вычисление положительных факториалов по действию очень похоже на действие возведения в степень... только множители различные... Исходя из полученных формул отрицательный факториал берется не только от отрицательного значения но и имеет смысл обратных значений для положительных факториалов N... Во всяком случае вполне возможно N!=(N+1)!/(N+1) 0!=1!/1=1 (-1)!=0!/(0)=1/(0)= 1 неделённая единица (-2)!=(-1)!/(-1)= 1/(-1)= -1 (-3)!=(-2)!/(-2)=(-1)/(-2)= 1/2 (-4)!=(-3)!/(-3)=(1/2)/(-3)= -1/6 (-5)!=(-4)!/(-4)=(-1/6)/(-4)= 1/24 (-6)!=(-5)!/(-5)=(1/24)/(-5)= -1/120... Интересно что получаются обратные значения Гамма функциям от отположительных значений когда Г(N+1)=N! Г(N+1)=N×Г(N)=N×(N-1)! Немного неожиданно... Получается что для отрицательных Г(-(N+1))=1/Г(N+1)=1/N! Но есть "проблема" со знаком... Видим что постоянно через один изменяется знак при делении "факториалов" от отрицательных значений... Предположу что нужно брать для отрицательных значений N значение по модулю (а для обобщения и для положительных значений N...) N!=(N+1)!/|N+1| (N-1)!=N!/|N| 0!=1/1=1 (-1)!=0!/0=1/0= 0 (относительный ноль) или безотносительно единица неделённая что более верно... Тогда следует (-2)!= (-1)!/|-1|=1 (-3)!=(-2)!/|-2|=1/2 (-4)!=(-3)!/|-3|=1/6 (-5)!=(-4)!/|-4|=1/24... Как видим получаем обратные величины факториалов для положительных значений N... но еще идет сдвиг на один ход относительно факториалов для положительных значений N... Смею предположить что отрицательные факториалы должны считаться по формуле N!=(N+1)!/|N|... Тогда (-1)!=0!/|-1|=1/1=1 (-2)!=(-1)!/|-2|=1/2 (-3)!=(-2)!/|-3|=1/6 (-4)!=(-3)!/|-4|=1/24 (-5)!=(-4)!/|-5|=1/120... и получается что эти значения численно равны коэффициентам для нахождения "обратного факториала"... Кстати по этой же формуле получается 0!=1!/0=1/0=1 единица неделённая что наверное будет более верно... Если уж быть совсем дерзким и исходить из того что график этих значений должен бы быть хоть немного математически красив то возможно факториалы от отрицательных значений должны бы быть и сами отрицательными... Но я пока не нахожу физического смысла отрицательным значениям факториалов... (самим факториалам от отрицательных чисел смысл проявился очень явно)... к тому же придется признать что тогда при этом 0!=1/0=0 равен относительному нулю... Но это пока мои личные фантазии... и в этом надо сначала разобраться... а перед этим хорошенько подумать... Мне все же ближе "вариант с модулями"...

[@kingjohan2353]

What language is this?

[@balancemyself]

I think I can't do math but when see those things correctly I got it easy.

[@akaBaye]

is this extension 2?

[@Stranger-ngl]

Excited 😊

[@hillydilly2582]

I am 11 years old and in Year 6, is this relevant to me?😅😅❤❤

[@virtusosmartphone]

wish Prof Woo was my math teacher

[@dsp6742]

Sir, why is the graph of y=x! so insanely weird?

[@nin10dorox]

...It's complicated. The extension to real numbers is the gamma function, if you want more information, but I've found that the stuff online is pretty hard to understand. You can understand why it goes to infinity at all the negative integers, though, because when you use the recursive definition for -1, you divide by 0, which goes to infinity. So any integers to the left of that have that division by 0 in them.

[@BayuSanjaya]

I want to see the graph of factorial

[@jockenineones7210]

You must be the best teacher ever!

[@watchableraven3517]

Okay.

[@shanthiganapathy4660]

How to find factorial of a decimal number say 1.4 factorial.. please help

[@notboboi9977]

the gamma function

[@louisrovegno542]

How does your recursive definition help you solve (11/2)!

[@allmight801]

It probably doesn't i think you need gamma function for that

[@gwenkoller5516]

THANK U!!!!!!!

[@dabloons4days]

genius

[@racquelsabesaje4562]

factorial

[@RoseteMonik]

please be my professor!!

[@davidsanders4463]

I know this is an old video, but I wish this guy was my math teacher in high school

[@racquelsabesaje4562]

5x4x3/3=20x3/3=60/3=20

[@WooSup111]

but why 0 factorial is 1? something multiply 0 must be 0.

[@AchtungBaby77]

There's two ways to look at it. The first is that zero factorial is just an empty product, which by definition, is 1. The second, which is slightly more intuitive, is to recall that n! counts the number of ways of arranging n distinct objects. If we have zero objects, then there's only ONE way of arranging them, which is to have no arrangement at all, so 0! = 1.

[@balancemyself]

But I am a arts student 😢

[@vinayakmishra3206]

And I haven't even opt for mathematics

[@funonthebun888]

There’s no body there!!!!!

[@MoyuGuy]

I live factorials? sorry !* 😏

[@MoyuGuy]

this isnt funny even a little bit. Like I think I get it but is that even a joke???

[@eccentricaste3232]

ni n1 n+1 n-1 = n-1 N +1 N-1 = 0 Bla bla bla